By the title "DE", is this a differential equation? Does your equation mean y''''+4y=0?
But the rest you understand?Originally Posted by Bert
Method 1) (Informal but it works!)
Thus, (square root),
Take square roots,
There are hence 4 possibilities (based on plus minus signs).
then by the same argument you get the same solutions, as before.
Method 2) (The is the elegant way. [My method if you are curious was to guess and play around with the roots cuz I was too lazy to work it out])
Express this in polar form,
Now apply, de Moivre's theorem
And the roots are,
one for each value of . And
You get your solutions.